Seminars

Home Schools Mathematics Seminars

TITLE: [GS_M_GT] The Application of Symplectic Homology to Powered Flyby Manoeuvres

ABSTRACT: Powered flybys are an important manoeuvre commenly used in space missions to increase the kinetic energy of the spacecraft as effective as possible. Proving in which situations such an manoeuvre exists can therefore be helpful for improving the design of future space missions. The goal of this talk is to show how one can use the tools developed in symplectic topology to prove the existence of such powered flyby orbits. In the first part we start by discussing the basic idea behind the powered flyby manoeuvre. After a short repetition of Hamiltonian dynamics we introduce the restricted three body problem and investigate its Levi-Civita regularisation. To finish the first part we will see how to describe the powered flybys mathematically and how we can use the specific properties of the Levi-Civita regularization to gain some more control over these orbits. In the second part we then focus more on the symplectic topology, i.e. we give the definition of the Lagrangian Rabinowitz Floer homology and discuss the main ideas behind this homology. With this new tool at hand, we can then go ahead an prove the main theorem of this talk, the existence of infinitely many powered flyby orbits in the restricted three body problem for all energies below the first Lagrange point.